3 Answers
3

Rem wanted to protect Misa and would kill Light if he let/caused Misa to die. Misa, however, was a good tool for Light and he could not kill her without raising suspicion towards himself.

Light also wanted L to die, but he could not kill him without knowing his real name. Rem could see everyone's name with her shinigami eyes, but would not kill anyone unless Misa was in trouble. So, Light put Misa in trouble and pressured Rem into killing L and Wastabi. As a result, Rem died and Light thought he had no more people in his way.

If Rem didn't kill L and Wastabi, Misa definitely would have been caught again and killed. There would have been a lot of suspicion towards Light, but he may have been able to talk himself out of it. If he did not, he would have died also. It was a gamble.

Misa Misa was a useful tool but, with Rem always wanting to protect her and began to really care for her Light couldn't use her in anyway that would put her endanger for Rem would kill him the first chance she got. In order to use Misa and kill L he got Misa taken in and "endanger" putting the blame on L that he had done it. Doing that and edging Rem to kill him in order to save Misa since she was the only creature that could see L's real name doing this was killing to birds with one stone that kept getting in the way of Light's "good work."